Find the sum of roots of the equation $\displaystyle (3x+1)(x-1)=15$
- $-\cfrac 23$
- $\cfrac 23$
- $\cfrac 32$
- $-\cfrac 32$
Reveal answer
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B
Correct answer
Explanation
Expanding (3x+1)(x-1)=15 gives 3x^2 - 3x + x - 1 = 15, which simplifies to 3x^2 - 2x - 16 = 0. The sum of the roots of a quadratic equation ax^2 + bx + c = 0 is -b/a. Here, the sum is -(-2)/3 = 2/3.
AI explanation
First, expand the given equation (3x + 1)(x - 1) = 15 to standard quadratic form, which results in 3x squared minus 2x minus 1 equals 15, and then 3x squared minus 2x minus 16 equals 0. For any quadratic equation ax squared plus bx plus c equals 0, the sum of its roots is given by the formula minus b divided by a. Substituting the coefficients a equals 3 and b equals minus 2 gives the sum as minus (minus 2) divided by 3. This simplifies to 2/3.